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Puzzle 10/10/31: B6 XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Sat Oct 30, 2010 5:37 pm    Post subject: Puzzle 10/10/31: B6 XY Reply with quote

I'm hanging up my hat on posting puzzles. Today's puzzles are the last.

Code:
 +-----------------------+
 | . . 3 | . . . | . . . |
 | . . 5 | . . . | 6 1 3 |
 | 7 8 6 | . 3 . | 5 . 4 |
 |-------+-------+-------|
 | . . . | 7 . . | 1 . . |
 | . . 7 | . 5 . | . 4 . |
 | . . . | . . 3 | . . 7 |
 |-------+-------+-------|
 | . 7 9 | 3 . . | 4 8 . |
 | . 6 . | . 8 . | 7 3 5 |
 | . 3 8 | . . 1 | . 6 . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Mon Nov 01, 2010 7:45 am    Post subject: Reply with quote

Looked like lots of ADP's but I rarely get lucky with them. Two steps...
Quote:
type 2 UR(59) r46c28 ; r3c8<>2, r45c9|r6c7<>2
w-wing(89) ; (9=8)r5c6 - r4c6=r4c9 - (8=9)r6c7 ; r6c4<>9, r5c9<>9
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Fri Nov 05, 2010 1:09 am    Post subject: Reply with quote

Same.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Fri Nov 12, 2010 9:20 pm    Post subject: Reply with quote

Type 2 UR(59)r46c28; r3c8<>2

Code:

 *--------------------------------------------------*
 | 1    4    3    | 69   69   5    | 28   7    28   |
 | 9    2    5    | 8    4    7    | 6    1    3    |
 | 7    8    6    | 1    3    2    | 5    9    4    |
 |----------------+----------------+----------------|
 | 3    59   24   | 7    69   489  | 1    25   689  |
 | 68   1    7    | 2    5    89   | 3    4    689  |
 | 68   59   24   | 469  1    3    | 89   25   7    |
 |----------------+----------------+----------------|
 | 5    7    9    | 3    2    6    | 4    8    1    |
 | 2    6    1    | 49   8    49   | 7    3    5    |
 | 4    3    8    | 5    7    1    | 29   6    29   |
 *--------------------------------------------------*


Kraken cell (689)r4c9; r5c9<>9
(6)r4c9-r5c9=r5c1-(6=8)r6c1-(8=9)r6c7;
||
(8)r4c9-(8=9)r6c7;
||
(9)r4c9;

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Sat Nov 13, 2010 6:46 am    Post subject: Reply with quote

Marty, here's how I find chains. By pure luck!!!

The following observation occurred by accident while I was considering Ted's grid after the UR Type 2.

There is a strong link on <9> in [c2]. This means that r4c5=9 and r6c7=9 can not both be true. Anything that would force them both true must itself be false. Consider r6c4=6:

Code:
 (6)r6c4 - (6=8)r6c1 - (8=9)r6c7
 (6)r6c4 -             (6=9)r4c5

This can be expanded to include the <59> cells in [c2],

Code:
 (6)r6c4 - (6=8)r6c1 - (8=9)r6c7 - (9=5)r6c2
 (6)r6c4 -             (6=9)r4c5 - (9=5)r4c2

and combined/wrapped into a discontinuous loop before finally being reduced to an XY-Chain.

Code:
 (6)r6c4 - (6=8)r6c1 - (8=9)r6c7 - (9=5)r6c2 - (5=9)r4c2 - (9=6)r4c5 - (6)r6c4

           (6=8)r6c1 - (8=9)r6c7 - (9=5)r6c2 - (5=9)r4c2 - (9=6)r4c5            =>  r6c4<>9
 +-----------------------------------------------------+
 |  1    4    3    |  69   69   5    |  28   7    28   |
 |  9    2    5    |  8    4    7    |  6    1    3    |
 |  7    8    6    |  1    3    2    |  5    9    4    |
 |-----------------+-----------------+-----------------|
 |  3    59   24   |  7    69   489  |  1    25   689  |
 |  68   1    7    |  2    5    89   |  3    4    689  |
 |  68   59   24   |  469  1    3    |  89   25   7    |
 |-----------------+-----------------+-----------------|
 |  5    7    9    |  3    2    6    |  4    8    1    |
 |  2    6    1    |  49   8    49   |  7    3    5    |
 |  4    3    8    |  5    7    1    |  29   6    29   |
 +-----------------------------------------------------+
 # 27 eliminations remain
___________________________________________________________________________________________

Yes, I make it look so easy -- NOT. _ Laughing _
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